Low-Complexity Algorithms for Trinion-Based Digital Signal Processing

This paper continues a series of publications devoted to low-complexity digital signal processing (DSP) algorithms using hypercomplex number systems. As in the previous cases, we are talking about three basic digital signal processing operations: the operation of multiplying two hypercomplex numbers, the operation of the dot product of two hypercomplex-valued vectors, and the operation of multiplying a hypercomplex number by a set of several other hypercomplex numbers. However, unlike the previous cases, the new algorithms use trinions as the underlying hypercomplex number system. To reduce the computational complexity of these operations, it is proposed to use the fast circular convolution algorithm, well known in digital signal processing. Using this algorithm reduces the number of multiplications and additions of real numbers required to perform calculations. Thus, the use of the proposed algorithms will speed up calculations in DSP applications using trinions.